Planting wheat after sorghum can be done successfully.  Wheat stands are most uniform when the sorghum crop is killed with glyphosate and at least a month or more has passed between sorghum harvest and wheat planting.

Grain sorghum produces various allelopathic compounds that have been known to inhibit certain pests.  Root exudates or compounds leaching from decomposing sorghum may affect growth of neighboring plants, and the concern is that there might be issues with rotational crops like wheat or cover crops.  However, colleagues in Arkansas and Mississippi indicate they have good luck planting wheat after sorghum in worked ground where the sorghum crop has been killed and several weeks have passed between sorghum harvest and planting of wheat.  Some of the suspected allelopathy may be nothing more than dry soil.  If sorghum plants are not shut down with glyphosate, green stems will continue to extract moisture from the soil for weeks after harvest until frost, causing soil to be even drier in a dry fall.